Diagonalization Algorithms

In his presentation in the Complexity and Linear Algebra Boot Camp, Senior Scientist Nikhil Srivastava defines the problem of approximately diagonalizing a given dense matrix, and explains two phenomena that impede the convergence of diagonalization algorithms and complicate their analysis: small eigenvalue gaps, and non-orthogonal eigenvectors (i.e., nonnormality). He goes on to explain how random perturbations can be used to surmount these difficulties, and surveys what is known and remains to be discovered in this area.